Question

Which of the following represents a geometric series (remember what a series is as opposed to a sequence)?

Answer 1

Answer:

4 + 12 + 36 + ...

Step-by-step explanation:

4, 12, 36, ... is a geometric sequence, it has a common ratio of $r=\frac{36}{12}=\frac{12}{4}=3$

When we add the terms of a geometric sequence we get a geometric series.

4+12+36+ ... is a geometric series, it has a common ratio of $r=\frac{36}{12}=\frac{12}{4}=3$

4 + 12 + 20 + ... is not a geometric series because it has no common ratio

$\frac{20}{12}\ne \frac{12}{4}$

The second choice is correct